Quote:
Originally Posted by Dr Sardonicus
It occurred to me to wonder how many times the block of decimal digits representing a prime p can reasonably be expected to occur before it occurs in its proper place in the sequence of primes.

Each sequence of n digits should occur equally often. Thus if you sequentially search for 50 6digit sequences, you should on average expect to have seen 50 of the last sequence  on average encountering it once before finding each of the earlier 49 ones.
So the expected number should be (number of earlier equally long target sequences) + (number of one earlier one digit shorter target sequences)/10 + (two shorter)/100 and so on.